Geographic privacy or geo-privacy refers to the keeping private of one's geographic location, especially the restriction of geographical data maintained by personal electronic devices. Geo-privacy is a crucial aspect of personal security; however, it often goes unnoticed in daily activities. With the surge in the use of Large Multimodal Models (LMMs), such as GPT-4, for Open Source Intelligence (OSINT), the potential risks associated with geo-privacy breaches have intensified. This study develops a location-integrated GPT-4 based model named GeoLocator and designs four-dimensional experiments to demonstrate its capability in inferring the locational information of input imageries and/or social media contents. Our experiments reveal that GeoLocator generates specific geographic details with high accuracy and consequently embeds the risk of the model users exposing geospatial information to the public unintentionally, highlighting the thread of online data sharing, information gathering technologies and LLMs on geo-privacy. We conclude with the broader implications of GeoLocator and our findings for individuals and the community at large, by emphasizing the urgency for enhanced awareness and protective measures against geo-privacy leakage in the era of advanced AI and widespread social media usage.